Page 40 - Wind Energy Handbook

14 THE WIND RESOURCE

records is a limitation, careful analysis by, for example, Palutikoff, Guo and
Halliday (1991) has demonstrated clear trends. Clearly these may be linked to long-
term temperature variations for which there is ample historical evidence. There is
also much debate at present about the likely effects of global warming, caused by
human activity, on climate, and this will undoubtedly affect wind climates in the
coming decades.
Apart from these long-term trends there may be considerable changes in windi-
ness at a given location from one year to the next. These changes have many causes.
They may be coupled to global climate phenomema such as el nin ˜o, changes in
atmospheric particulates resulting from volcanic eruptions, and sunspot activity, to
name a few. These changes add significantly to the uncertainty in predicting the
energy output of a wind farm at a particular location during its projected lifetime.

2.4 Annual and Seasonal Variations

While year-to-year variation in annual mean wind speeds remains hard to predict,
wind speed variations during the year can be well characterized in terms of a
probability distribution. The Weibull distribution has been found to give a good
representation of the variation in hourly mean wind speed over a year at many
typical sites. This distribution takes the form

k !
U
F(U) ¼ exp (2:1)
c

where F(U) is the fraction of time for which the hourly mean wind speed exceeds
U. It is characterized by two parameters, a ‘scale parameter’ c and a ‘shape
parameter’ k which describes the variability about the mean. c is related to the
annual mean wind speed U by the relationship

U ¼ cˆ(1 þ 1=k) (2:2)

where ˆ is the complete gamma function. This can be derived by consideration of
the probability density function
!
k
dF(U) U k 1 U
f(U) ¼ ¼ k exp (2:3)
dU c k c

since the mean wind speed is given by
ð 1
U ¼ Uf(U)dU (2:4)
0

A special case of the Weibull distribution is the Rayleigh distribution, with k ¼ 2,
which is actually a fairly typical value for many locations. In this case, the factor